An established technique in the field of the above mentioned type of apparatus is based on the idea of feeding the web which has run out and the new one between a pair of rollers which are brought together so as to bring the first web into contact with the second thereby splicing them by putting a suitable adhesive between them. This adhesive is commonly provided by a transverse double-sided adhesive tape previously applied manually by an operator to the leading end of the new web. This double-sided adhesive tape is the source of considerable problems due to the fact that, as the area of contact of the rollers is usually inaccessible, it is necessary to make special provision for the tape to be applied to the web at a point which is convenient for the operator to carry out the necessary manipulation. Moreover the subsequent positioning of the end of the new web between the rollers requires special care inasmuch as there is a need to avoid the tape which has been applied to the new web becoming stuck to parts of the equipment when it is fed between the rollers, thereby making subsequent splicing impossible without replacing the tape. The above mentioned problems are made even worse when the webs are of any significant width, since in this case the web does not have much transverse rigidity and is inclined to bend.